Answer
$$\frac{2\sqrt{5}}{3\sqrt{3}\cdot6}=\frac{\sqrt{15}}{27}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{5}}{3\sqrt{3}\cdot6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{5}}{3\sqrt{3}\cdot6}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{15}}{54} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{15}}{27}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{5} } \cdot \sqrt{3} = 2 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ 18 \sqrt{3} } \cdot \sqrt{3} = 54 $$ |
| ③ | Divide both numerator and denominator by 2. |
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